A radar sensor which ascertains the distance and relative speed of vehicles traveling ahead and regulates the velocity of one's own vehicle is known from “Adaptive Cruise Control (ACC),” published by Robert Bosch GmbH in Apr. 2002 (ISBN-3-7782-2034-9). If a vehicle traveling ahead is detected, the vehicle velocity is controlled in the manner of a constant-distance regulating function so that one's own vehicle follows the vehicle traveling ahead at a predetermined distance. If no vehicle is detected ahead, the velocity is regulated in the manner of a constant-velocity regulating function, the vehicle velocity being adjusted to a setpoint velocity preset by the driver.